Speak to a counsellor about this. A lot of people have social anxiety, especially those just starting university but you'll never be able to deal with it without going out of your comfort zone at times in order to expand it. You can either try to just avoid situations that make you anxious, which doesn't address the problem, or try to get to the point where you can do what you want despite the anxiety (if needed consider therapy/medication)
If you really enjoy the university, maybe consider commuting for a bit to get used to it and then slowly transition to moving rather than moving in straight away. You shouldn't be in university more than 2-3 days anyway. Otherwise, are there any local universities you like?